Evaluate
-8+12i
Real Part
-8
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1\times 2+1\times \left(2i\right)+5i\times 2+5\times 2i^{2}
Multiply complex numbers 1+5i and 2+2i like you multiply binomials.
1\times 2+1\times \left(2i\right)+5i\times 2+5\times 2\left(-1\right)
By definition, i^{2} is -1.
2+2i+10i-10
Do the multiplications.
2-10+\left(2+10\right)i
Combine the real and imaginary parts.
-8+12i
Do the additions.
Re(1\times 2+1\times \left(2i\right)+5i\times 2+5\times 2i^{2})
Multiply complex numbers 1+5i and 2+2i like you multiply binomials.
Re(1\times 2+1\times \left(2i\right)+5i\times 2+5\times 2\left(-1\right))
By definition, i^{2} is -1.
Re(2+2i+10i-10)
Do the multiplications in 1\times 2+1\times \left(2i\right)+5i\times 2+5\times 2\left(-1\right).
Re(2-10+\left(2+10\right)i)
Combine the real and imaginary parts in 2+2i+10i-10.
Re(-8+12i)
Do the additions in 2-10+\left(2+10\right)i.
-8
The real part of -8+12i is -8.
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